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TRS_Innermost 2019-03-28 22.12 pair #432271159
details
property
value
status
complete
benchmark
PEANO_nokinds_GM.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n018.star.cs.uiowa.edu
space
Transformed_CSR_innermost_04
run statistics
property
value
solver
muterm 6.0.3
configuration
default
runtime (wallclock)
1.55981 seconds
cpu usage
1.38622
user time
1.04177
system time
0.34445
max virtual memory
707684.0
max residence set size
11276.0
stage attributes
key
value
starexec-result
YES
output
1.34/1.55 YES 1.34/1.55 1.34/1.55 Problem 1: 1.34/1.55 1.34/1.55 (VAR v_NonEmpty:S M:S N:S V1:S V2:S X:S X1:S X2:S X3:S) 1.34/1.55 (RULES 1.34/1.55 a__U11(tt,N:S) -> mark(N:S) 1.34/1.55 a__U11(X1:S,X2:S) -> U11(X1:S,X2:S) 1.34/1.55 a__U21(tt,M:S,N:S) -> s(a__plus(mark(N:S),mark(M:S))) 1.34/1.55 a__U21(X1:S,X2:S,X3:S) -> U21(X1:S,X2:S,X3:S) 1.34/1.55 a__and(tt,X:S) -> mark(X:S) 1.34/1.55 a__and(X1:S,X2:S) -> and(X1:S,X2:S) 1.34/1.55 a__isNat(0) -> tt 1.34/1.55 a__isNat(plus(V1:S,V2:S)) -> a__and(a__isNat(V1:S),isNat(V2:S)) 1.34/1.55 a__isNat(s(V1:S)) -> a__isNat(V1:S) 1.34/1.55 a__isNat(X:S) -> isNat(X:S) 1.34/1.55 a__plus(N:S,0) -> a__U11(a__isNat(N:S),N:S) 1.34/1.55 a__plus(N:S,s(M:S)) -> a__U21(a__and(a__isNat(M:S),isNat(N:S)),M:S,N:S) 1.34/1.55 a__plus(X1:S,X2:S) -> plus(X1:S,X2:S) 1.34/1.55 mark(0) -> 0 1.34/1.55 mark(U11(X1:S,X2:S)) -> a__U11(mark(X1:S),X2:S) 1.34/1.55 mark(U21(X1:S,X2:S,X3:S)) -> a__U21(mark(X1:S),X2:S,X3:S) 1.34/1.55 mark(and(X1:S,X2:S)) -> a__and(mark(X1:S),X2:S) 1.34/1.55 mark(isNat(X:S)) -> a__isNat(X:S) 1.34/1.55 mark(plus(X1:S,X2:S)) -> a__plus(mark(X1:S),mark(X2:S)) 1.34/1.55 mark(s(X:S)) -> s(mark(X:S)) 1.34/1.55 mark(tt) -> tt 1.34/1.55 ) 1.34/1.55 (STRATEGY INNERMOST) 1.34/1.55 1.34/1.55 Problem 1: 1.34/1.55 1.34/1.55 Dependency Pairs Processor: 1.34/1.55 -> Pairs: 1.34/1.55 A__U11(tt,N:S) -> MARK(N:S) 1.34/1.55 A__U21(tt,M:S,N:S) -> A__PLUS(mark(N:S),mark(M:S)) 1.34/1.55 A__U21(tt,M:S,N:S) -> MARK(M:S) 1.34/1.55 A__U21(tt,M:S,N:S) -> MARK(N:S) 1.34/1.55 A__AND(tt,X:S) -> MARK(X:S) 1.34/1.55 A__ISNAT(plus(V1:S,V2:S)) -> A__AND(a__isNat(V1:S),isNat(V2:S)) 1.34/1.55 A__ISNAT(plus(V1:S,V2:S)) -> A__ISNAT(V1:S) 1.34/1.55 A__ISNAT(s(V1:S)) -> A__ISNAT(V1:S) 1.34/1.55 A__PLUS(N:S,0) -> A__U11(a__isNat(N:S),N:S) 1.34/1.55 A__PLUS(N:S,0) -> A__ISNAT(N:S) 1.34/1.55 A__PLUS(N:S,s(M:S)) -> A__U21(a__and(a__isNat(M:S),isNat(N:S)),M:S,N:S) 1.34/1.55 A__PLUS(N:S,s(M:S)) -> A__AND(a__isNat(M:S),isNat(N:S)) 1.34/1.55 A__PLUS(N:S,s(M:S)) -> A__ISNAT(M:S) 1.34/1.55 MARK(U11(X1:S,X2:S)) -> A__U11(mark(X1:S),X2:S) 1.34/1.55 MARK(U11(X1:S,X2:S)) -> MARK(X1:S) 1.34/1.55 MARK(U21(X1:S,X2:S,X3:S)) -> A__U21(mark(X1:S),X2:S,X3:S) 1.34/1.55 MARK(U21(X1:S,X2:S,X3:S)) -> MARK(X1:S) 1.34/1.55 MARK(and(X1:S,X2:S)) -> A__AND(mark(X1:S),X2:S) 1.34/1.55 MARK(and(X1:S,X2:S)) -> MARK(X1:S) 1.34/1.55 MARK(isNat(X:S)) -> A__ISNAT(X:S) 1.34/1.55 MARK(plus(X1:S,X2:S)) -> A__PLUS(mark(X1:S),mark(X2:S)) 1.34/1.55 MARK(plus(X1:S,X2:S)) -> MARK(X1:S) 1.34/1.55 MARK(plus(X1:S,X2:S)) -> MARK(X2:S) 1.34/1.55 MARK(s(X:S)) -> MARK(X:S) 1.34/1.55 -> Rules: 1.34/1.55 a__U11(tt,N:S) -> mark(N:S) 1.34/1.55 a__U11(X1:S,X2:S) -> U11(X1:S,X2:S) 1.34/1.55 a__U21(tt,M:S,N:S) -> s(a__plus(mark(N:S),mark(M:S))) 1.34/1.55 a__U21(X1:S,X2:S,X3:S) -> U21(X1:S,X2:S,X3:S) 1.34/1.55 a__and(tt,X:S) -> mark(X:S) 1.34/1.55 a__and(X1:S,X2:S) -> and(X1:S,X2:S) 1.34/1.55 a__isNat(0) -> tt 1.34/1.55 a__isNat(plus(V1:S,V2:S)) -> a__and(a__isNat(V1:S),isNat(V2:S)) 1.34/1.55 a__isNat(s(V1:S)) -> a__isNat(V1:S) 1.34/1.55 a__isNat(X:S) -> isNat(X:S) 1.34/1.55 a__plus(N:S,0) -> a__U11(a__isNat(N:S),N:S) 1.34/1.55 a__plus(N:S,s(M:S)) -> a__U21(a__and(a__isNat(M:S),isNat(N:S)),M:S,N:S) 1.34/1.55 a__plus(X1:S,X2:S) -> plus(X1:S,X2:S) 1.34/1.55 mark(0) -> 0 1.34/1.55 mark(U11(X1:S,X2:S)) -> a__U11(mark(X1:S),X2:S) 1.34/1.55 mark(U21(X1:S,X2:S,X3:S)) -> a__U21(mark(X1:S),X2:S,X3:S) 1.34/1.55 mark(and(X1:S,X2:S)) -> a__and(mark(X1:S),X2:S) 1.34/1.55 mark(isNat(X:S)) -> a__isNat(X:S) 1.34/1.55 mark(plus(X1:S,X2:S)) -> a__plus(mark(X1:S),mark(X2:S)) 1.34/1.55 mark(s(X:S)) -> s(mark(X:S)) 1.34/1.55 mark(tt) -> tt 1.34/1.55 1.34/1.55 Problem 1: 1.34/1.55 1.34/1.55 SCC Processor: 1.34/1.55 -> Pairs: 1.34/1.55 A__U11(tt,N:S) -> MARK(N:S) 1.34/1.55 A__U21(tt,M:S,N:S) -> A__PLUS(mark(N:S),mark(M:S)) 1.34/1.55 A__U21(tt,M:S,N:S) -> MARK(M:S) 1.34/1.55 A__U21(tt,M:S,N:S) -> MARK(N:S) 1.34/1.55 A__AND(tt,X:S) -> MARK(X:S) 1.34/1.55 A__ISNAT(plus(V1:S,V2:S)) -> A__AND(a__isNat(V1:S),isNat(V2:S)) 1.34/1.55 A__ISNAT(plus(V1:S,V2:S)) -> A__ISNAT(V1:S) 1.34/1.55 A__ISNAT(s(V1:S)) -> A__ISNAT(V1:S) 1.34/1.55 A__PLUS(N:S,0) -> A__U11(a__isNat(N:S),N:S) 1.34/1.55 A__PLUS(N:S,0) -> A__ISNAT(N:S) 1.34/1.55 A__PLUS(N:S,s(M:S)) -> A__U21(a__and(a__isNat(M:S),isNat(N:S)),M:S,N:S) 1.34/1.55 A__PLUS(N:S,s(M:S)) -> A__AND(a__isNat(M:S),isNat(N:S)) 1.34/1.55 A__PLUS(N:S,s(M:S)) -> A__ISNAT(M:S) 1.34/1.55 MARK(U11(X1:S,X2:S)) -> A__U11(mark(X1:S),X2:S) 1.34/1.55 MARK(U11(X1:S,X2:S)) -> MARK(X1:S)
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